5,755 research outputs found
On a Refined Stark Conjecture for Function Fields
We prove that a refinement of Stark's Conjecture formulated by Rubin is true
up to primes dividing the order of the Galois group, for finite, abelian
extensions of function fields over finite fields. We also show that in the case
of constant field extensions a statement stronger than Rubin's holds true
Brauer Groups and Tate-Shafarevich Groups
Let XK be a proper, smooth and geometrically connected curve over a global field K. In this paper we generalize a formula of Milne relating the order of the Tate-Shafarevich group of the Jacobian of XK to the order of the Brauer group of a proper regular model of XK. We thereby partially answer a question of Grothendieck
Algebraic cycles on Severi-Brauer schemes of prime degree over a curve
Let be a perfect field and let be a prime number different from the
characteristic of . Let be a smooth, projective and geometrically
integral -curve and let be a Severi-Brauer -scheme of relative
dimension . In this paper we show that contains
a subgroup isomorphic to for every in the range . We deduce that, if is a number field, then is finitely
generated for every in the indicated range.Comment: 6 page
Finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves
We obtain finiteness theorems for algebraic cycles of small codimension on
quadric fibrations X over curves over perfect fields k. For example, if k is
finitely generated over Q and the fibration has odd relative dimension at least
11, then CH^{i}(X) is finitely generated for i<=4.Comment: 13 page
- …